Name ___________________________
AB Calculus
Cross – Sectional Volume
1. Find the volume of a solid whose base is the region inside the circle
and the cross sections taken are perpendicular to the x-axis are equilateral
triangles.
4
2. Find the volume of a solid whose base is the region inside the circle
and the cross sections taken are perpendicular to the x-axis are isosceles right
triangles with bases lying along the base of the circle.
4
3. Find the volume of a solid whose base is the region inside the circle
and the cross sections taken are perpendicular to the x-axis are isosceles right
triangles whose hypotenuse lying along the base of the circle.
4. The base of a solid is the region bounded by the graphs of f  x   x 2 and
4
g x   8  x 2
a. Find the volume of the solid if all cross sections perpendicular to the x-axis are
squares.
b. Find the volume of all of the cross sections perpendicular to the x-axis are
semicircles.
5. Find the volume of a solid which lies between the functions
whose cross sections are squares perpendicular to the y-axis
and
2
6. A solid has its base is the region bounded by the lines x + 2y = 6, x = 0 and y = 0 and
the cross sections taken perpendicular to y-axis are circles. Find the volume the solid.
7. A solid has its base is the region bounded by the lines x + y = 4, x = 0 and y = 0 and
the cross section is perpendicular to the x-axis are equilateral triangles. Find its volume.
8. Let the first quadrant region enclosed by the graph of
and the lines x=1 and x=4
be the base of the solid. If cross sections perpendicular to the x-axis are semicircles, the
volume of the solid is
(A)
(B)
(C)
(D)
(E)
9. Let the base of a solid be the first quadrant region enclosed by the x-axis, the -axis, the
y-axis and the graph of
1
. If all the cross sections perpendicular to the y-axis
are squares, the volume of the solid is
(A) 3 units3
(B) 2 units3
(C) 1 units3
(D) ½ units3
(E) 1/3 units3
10. A solid as its base the region enclosed by the graph of
between
and
cos and the x-axis
. If every cross section perpendicular to the x-axis is a
square, the volume of the solid is
(A)
(B)
(C)
(D)
(E) 2
HOMEWORK: pg 390 2, 4, 8